The present invention relates to an astronomical globe and more particularly to an automatic tracking astronomical globe that can be used to find the positions of the sun, moon, and prominent stars at any time from a fixed position on the earth.
The automatic tracking astronomical globe of the present invention is based on the concept of the celestial sphere known since antiquity.
Referring to FIG. 1 of the drawings the celestial sphere 100 is an imaginary sphere of infinite radius with the earth 200 at its center. Stars grouped into the well known constellations 300 of the zodiac were assummed to be affixed to celestial sphere 100 which rotates in a clockwise or easterly direction relative to earth 200, completing one revolution in a sidereal day.
A sidereal day having a period of 23 hours, 56 minutes, and 3 seconds, or about 4 minutes shorter than our 24 hour civil day which is based on the position of the sun.
As the true distance of stars away from the planet earth are now known to be measured in light-years, this model is sufficiently accurate for many viewing purposes.
The only apparent motion of the fixed stars was in circular paths called diurnal circles, due to the daily rotation of the celestial sphere which we now know of course to be due to the earth's rotation.
An equatorial coordinate system is used to determine the position of a star on the celestial sphere of similarity with the system of longitudes and latitudes used to determine positions on the surface of the earth.
The celestial latitude or declination A of a star is measured from the celestial equator 101 of celestial sphere 100 which is defined by the projection of the earth's equator 201 thereon. The declination is measured in degrees from 0 degrees on celestial equator 101 to + or -90 degrees to the respective north and south celestial poles, 102a and 102b.
Our longitude co-ordinates on earth are defined in terms of degrees east or west of the prime meridian circle 202 passing through Greenwich Observatory in England. However, on the celestial sphere a different reference based on the vernal equinox 103a is used.
Vernal equinox 103a and autumnal equinox 103b, diametrically opposite from it on celestial sphere 100, are defined by the intersection of celestial equator 101 and the circle of the ecliptic 104.
Ecliptic 104 represents the apparent path of the sun around the celestial sphere. As the earth revolves around the sun, the sun appears to shift slowly eastwards from its position in the sky, returning to the same position after a sidereal year, having a period of about 365.265 civil days, which is slightly more than 6 hours longer than a 365 day civil year.
Ecliptic 104 assumes an angle of about 23.5 degrees with respect to celestial equator 101 due to the tilt of the earth's axis relative to the rotational plane of its orbit about the sun.
The autumnal and vernal equinoxes, 103a and 103b, correspond to the times in fall and spring, respectively, when the sun is at celestial equator 101 and we have days and nights of equal duration.
The tropical year, which accurately tracks the changes in the seasons and is the basis of the Gregorian calender used worldwide, has a length of about 365.242 civil days, or slightly less than 6 hours longer than a 365 day civil year.
The Gregorian calender with its system of an intercalated day, i.e. a Febuary 29th, on leap years with a 4 year cycle with the exception of century years divisible by 400, closely approximates the 365.242 day tropical year on average, so that the seasons do not become out of step with the dates on the calender.
The sidereal year is some 20 minutes longer than the tropical year as the sidereal year takes into account the slow precession of the earth's axis, which is similar to the gyration of a spinning top.
The celestial longitude or right ascension B of a celestial object is measured in terms of hours, minutes, and seconds from the vernal equinox instead of degrees, with one hour being the equivalent of 15 degrees, 24 hours equaling a full 360 degree sweep back to the origin.
The dog star Sirius at point 4, for example, is the brightest star in the sky and has a declination of -16 degrees and 39 minutes and a right ascension of 6 hours, 42 minutes, and 54 seconds.
Astronomers keep time with a sidereal clock and a star of the same declination as the latitude of an observation point on the earth is directly overhead when its right ascension matches the local sidereal time.
The moon can also be represented on the celestial sphere, but like the sun moves slowly eastward across the celestial sphere, due to its orbit about the earth. The plane of its orbit assumes an angle of about 5.2 degrees with respect to the ecliptic, with the moon completing one orbit in about 27.322 civil days to define a sidereal month.
While the sidereal month accurately represents the cycle of change of the position of the moon on the celestial sphere, the synodic month accurately represents the cycle of the lunar phases, having a period of about 29.531 civil days. In that period of time the moon proceeds from the phase of a new moon to a full moon and back again to a new moon.
The synodic month is longer than the sidereal month due to the change in the earth's position relative to the sun as the moon moves along its orbit, the lunar phase being a function of the relative angles between the earth, sun, and moon.
The Chinese lunar calender, which is actually based on both solar and lunar cycles, is used concurrently with the Gregorian calender in many parts of Asis, and has months based on the synodic cycle.
The new moon and full moon always fall on the first and fifteenth day of a chinese lunar month, respectively. As the synodic period is an irrational fraction of a day in excess of 29 days in length, the Chinese lunar calender comprises a non-periodic sequence of long months with 30 days and short months with 29 days, with the sequence of long and short months in a 12 month year varying from year to year.
The Chinese lunar calender also uses a sequence of 24 fortnightly periods, which include the beginnings of the seasons, equinoxes, and solstices of the western calender, that divides the tropical year into 24 periods with each period representing a 15 degree motion of the sun along the path of the ecliptic.
The periods are actually longer than a fortnight and average 15.218 days in length, the varying length of the periods being due to the elliptic orbit of the earth about the sun, with the sun moving through different 15 degree sectors on the ecliptic at different speeds.
The 24 fortnightly periods would of course fall on different dates on the Chinese lunar calender from one year to the next. On average, after every 33 months an extra month must be intercalated into the normal 12 months to contain all 24 fortnightly periods in the same year, thus keeping the chinese lunar calender in step with the seasons.
Though the equatorial co-ordinates discussed above are useful for reference and calculation, astronomers in the field or amateur stargazers use a different set of co-ordinates to point their telescopes or viewing instruments.
Referring to FIG. 2, an observer on any point of the earth, could with the aid of a compass and a level or plumb bob, determine his or her meridian circle 5 and zenith 6. Zenith 6 is the point directly overhead on celestial sphere 100 from a given location on earth. A line containing that location and its zenith passes through the earth's center.
The observer's meridian circle 5 is a circle containing the north and south celestial poles and lies on the same plane as the observer's location.
Telescope 7 is pointed towards a celestial object with the guidance of a set of horizon co-ordinates. The telescope is rotated in a horizontal plane from 0 to 360 degrees from the southern direction, according to an azimuth angle C, and in a vertical plane from 0 degrees, pointing towards celestial horizon 105, to 90 degrees, pointing towards zenith 6, according to an elevation angle D.
Whereas, the equatorial co-ordinates given in star charts and tables are fixed points on the celestial sphere, the azimuth angle C and elevation angle D of a celestial object varies with the longitude and latitude of the observation point and also with time.
Though it is possible to calculate the local azimuth and elevation of a celestial object given its equatorial co-ordinates and the latitude and longitude of the location, a sidereal clock would also have to be at hand or calculation of the sidereal time from the local civil time would have to be done. This process tends to be tedius even with an electronic calculator, and takes away from the spirit of stargazing.
The automatic astronomical globe of the present invention however offers to a user a self contained model of the celestial sphere that once initially calibrated for his or her location will automatically and graphically reveal the positions of the fixed stars, sun, and moon and allow the quick determination of their local azimuth and elevation in step with the change of sidereal time.
Though clock-driven celestial globes have been provided in the past, some even with representation of the motion of the sun and moon, none offer the ease of initial calibration and possibility of adjustment as provided by the automatic tracking astronomical globe of the present invention.
Moreover, the automatic tracking astronomical globe of the present invention provides a means of quickly determining the horizon co-ordinates of any object on the celestial globe thereof, and an integral Gregorian and Chinese lunar calenders, the latter of which also indicates the lunar phases.